⡍⢎⡱⢡⢊⠴⢡⠢⣑⠂⠖⣠⠒⡰⢠⠃⢆⡱⠌⢢⠐⢂⢄⣦⣤⠦⠼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⢴⣀⢆⡐⠢⡐⠰⡐⢂⠆⡱⢀⠖⡠ ⡜⢢⠜⡡⢎⠲⠥⡒⠥⡚⠴⢡⠚⡔⢣⠘⣆⠲⣉⠆⣉⠢⡘⢧⡀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠶⣶⣶⣶⠶⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⡀⣀⣬⣟⣀⡃⢅⠓⡌⠣⠜⡠⢃⠎⡔ ⣌⠢⡙⡔⣊⠕⣢⠙⢦⡑⢪⠱⡘⡔⠣⢎⠤⡓⡄⡊⢄⠆⡑⠦⣹⠆⢀⢀⣴⡾⠟⠉⠀⠀⢀⣾⣿⣿⠉⠀⢸⡉⢿⠿⣿⣶⣤⡐⢦⣀⠵⠿⣿⣿⡿⠛⡄⢫⢐⡃⢎⡐⢣⠘⡤ ⣦⠵⣥⣚⠤⠯⠴⡭⢦⡙⢦⢣⡝⡬⢳⢌⠶⡱⢦⠭⢮⡜⣵⣟⣁⡀⢯⣾⣿⡷⠀⠀⠀⠀⣼⣿⠿⠟⣀⣀⡷⡘⢦⣻⣿⣿⣿⣿⣰⡐⠦⡘⢌⣻⡴⣥⢬⡵⢦⡼⠴⣬⠵⢮⡴ ⣯⢟⡶⣍⢻⣙⠳⡜⢦⡙⣦⢳⡼⣱⢏⡾⣹⡝⣯⣛⣧⢟⡾⣹⣿⣥⣼⣿⣿⣧⣴⣤⣶⠿⠿⠟⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠻⢿⣿⡿⣱⢏⡾⡼⢧⡻⣝⢮⣛⢧⣛ ⣏⢿⡸⣇⢇⡏⢷⣉⢷⡹⣶⣏⣸⣇⣿⣸⣇⣿⣱⣏⣾⣉⣿⣹⣎⣷⣿⣿⣿⣿⠿⠿⠿⣶⡀⠀⠀⡀⣰⡿⠏⠁⠀⠀⠉⠿⣿⣿⣿⣷⣿⣿⣿⡶⠿⡾⢷⠿⢷⠿⡾⢷⢹⠾⡹ ⣟⢮⡳⣝⢮⣛⢷⣪⢧⣻⠞⠁⢢⡜⢠⠒⡨⠔⡡⢆⠢⡑⢢⠡⡌⠄⣿⡿⠋⠀⣀⣀⣄⣉⣡⠀⠀⠘⢏⢀⣤⠤⠤⠄⠀⠀⠸⡟⣿⣿⠛⡛⠡⢌⠂⡅⢢⠑⡪⠰⠡⢎⠢⣡⠃ ⣯⢷⡹⣎⡷⣹⡖⣯⠟⠁⡐⡈⠄⣸⠤⠥⢤⠱⢤⠬⠥⡜⠤⢥⠸⡔⣿⡇⠀⠀⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠟⡡⠚⣧⢐⡡⢂⠲⡐⢢⠒⣡⠒⡥⢒⠒⢤⢃ ⡟⣶⡹⣎⢷⣳⡟⢁⠐⠠⠁⣰⢞⡱⣊⠝⣤⢋⠦⡙⢦⡉⢞⠤⡓⡜⣸⣇⠔⠒⠈⠁⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⠉⠉⠐⠒⠄⠰⣱⠀⣿⣷⣔⠣⡑⢬⢁⠳⣄⠫⢔⡉⠞⣠⢃ ⣟⢶⣹⢞⡽⠃⢀⠂⠌⣰⠞⡍⢦⠱⡘⡜⢤⢋⠖⡩⢆⡹⢈⢖⡩⢒⣽⡇⢠⠔⠃⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠉⠒⠂⢤⡀⢀⡴⡻⢠⣿⣿⣿⢢⢙⢂⠎⡱⢌⢃⠎⡜⡱⢂⠣ ⣯⣟⠾⠋⡀⠂⠄⢈⡼⣿⣿⣌⠆⣣⢑⡚⡴⣉⠎⣕⠪⠴⣉⠦⣑⠣⠼⣿⠁⠀⣠⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠐⢄⡀⠀⠈⡌⠳⣾⣿⣿⣿⣿⠢⢍⢪⡘⢥⡉⢎⡜⡰⢡⢋⡜ ⡿⠊⢀⠐⠠⠁⡼⠋⢠⠉⠿⣾⣷⣄⠣⡜⡰⢡⠞⡤⢋⠵⡘⢦⠱⣉⠞⡬⢇⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢄⣸⠖⣾⡝⢿⣿⣿⣇⡍⢆⢣⠜⣢⠙⢦⡘⢥⠓⣌⠲ ⠀⠄⠠⠈⣠⠟⢀⠡⠂⡔⢀⠉⢻⣯⣷⡌⢱⢃⠞⣰⠩⢖⡩⢆⠏⡆⢯⣰⠯⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢃⣼⣷⠸⡡⢏⡻⠿⢎⡜⢢⠝⡤⢛⡤⡙⢦⡙⢤⠓ ⠐⠂⣀⣾⣅⠀⠂⠆⡑⠨⠠⠌⡠⠘⢻⣿⣦⡉⢎⠥⣋⠦⣑⠎⣜⠟⠭⣄⡀⠈⠟⣶⣄⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢻⢱⣶⠋⠙⢳⡝⡢⢕⣩⠲⡘⡥⢚⡌⢇⡲⣉⠦⡙⣌⠣ ⠀⡁⡾⢿⣿⣿⣦⡐⠠⢁⠡⢊⡐⠈⠤⡙⢿⣿⠮⠶⠤⢷⣌⡚⣼⠀⠀⡎⠏⠓⢖⠠⡽⢿⣲⣤⣄⣤⡶⣛⣊⣁⣀⠾⠥⠔⠊⠁⠀⣷⢡⢃⢆⠣⡕⣌⠣⡜⢢⠱⢌⠲⢱⡈⢇ ⠀⠄⠁⠀⠹⣻⣿⣿⣷⣄⡈⠄⡰⢉⡐⠰⡈⢻⠋⠉⠉⢻⠻⣷⣇⠀⠀⠠⡞⡄⠀⠈⠉⠉⠉⠉⠙⢒⡭⣇⣀⡀⠀⢀⣀⡀⠀⠀⢠⢸⠧⢯⠬⠧⠷⠬⠷⠭⠭⠟⠾⠽⠳⠿⠿ ⠀⠆⠀⠀⠀⠈⠱⡿⣿⣿⣿⣆⠰⠀⡈⢁⠰⢹⠁⠀⠀⢸⠀⣸⠉⡰⠀⡇⡾⠁⠀⠀⠀⠀⠀⠀⢰⡏⣰⡿⡆⠀⢀⡰⠈⡹⠀⢀⠇⡾⡁⢆⠸⢀⠁⠎⡰⠈⠰⡈⠰⢀⠇⠰⡀ ⠀⠂⠄⠀⠀⠀⠀⠀⠙⠽⣿⣿⣿⣦⣈⠢⠑⢸⠀⠀⢀⣴⣿⣿⣧⣅⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⡷⣞⣳⠺⡿⢊⠔⠀⠀⠸⢰⢸⣿⣶⣄⡂⠌⡐⢀⠁⠂⠄⡁⠂⠌⡐⠄ ⠀⠂⡄⠀⠀⠀⠀⠀⠀⠀⠈⢞⣿⢿⣿⣷⣌⣐⣠⣶⣿⡿⡿⠿⠿⠿⡟⠀⠀⠠⠤⡄⠀⠀⠀⠀⡤⣤⡀⠀⠀⠀⢸⠁⠀⠀⠀⢨⣦⣿⣿⣿⡿⢛⣖⣦⡈⠄⡉⠐⠠⠈⡐⠄⠃ ⠀⡁⣿⣶⣤⣀⠀⠀⠀⠀⠀⡄⣿⣀⡹⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠈⠀⣤⣤⡄⠀⠁⠀⠀⠀⠀⠀⢸⠀⣀⣠⣤⣾⣿⣿⣿⣿⢿⣼⡌⣿⣷⠀⠄⠁⢂⠡⠐⢈⠁ ⠠⢀⣿⣿⡿⠿⣷⣦⠄⠤⠐⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠀⠀⠀⢈⣍⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡷⣿⣿⣇⠠⠐⠀⠀⠌⠀⠂ ⠀⠀⡿⣀⢥⡄⠀⠈⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠣⡀⠀⠀⠘⣿⣿⣿⣿⣶⡶⠀⠀⠀⠀⠔⡇⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⢏⣻⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠾⣍⣠⣶⠶⣀⣀⣀⣀⠤⣤⣤⡶⢶⡤⣶⣤⡤⣤⠤⠤⢤⣀⠀⠈⠐⠄⢀⢹⣿⣙⣹⡟⠀⢀⠀⠐⡡⠜⠀⠀⠀⠈⢻⣿⣿⡿⠿⣛⠿⣿⣟⠶⣾⣿⣛⠙⠉⠛⠙⠉⠛ ⠀⠀⠀⠀⠀⠀⠈⠉⡼⡑⢦⡉⣾⡷⣋⠖⡼⢛⡍⡞⣼⠡⢎⡱⢊⠦⣩⢓⠲⢤⡈⢦⡁⡒⢊⣠⡦⠃⠐⠉⠀⠰⠁⠀⠀⠀⠘⡞⡥⣧⣿⡟⡰⣉⠿⣷⣸⣿⣏⠀⠀⡀⢀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⢠⢣⡙⢆⡱⢃⠖⣡⠚⡔⢣⡼⣹⢣⡙⢦⠱⣉⠖⡡⢎⡵⠋⠉⠒⠒⠭⠭⠅⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠘⣷⡿⣋⠲⡱⢌⠎⣿⣿⣽⣴⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡇⡜⢢⠱⣉⠞⡤⢋⡜⣡⡇⣏⠦⡑⢎⡱⢌⢎⡱⡺⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⢹⠾⣛⡳⣕⢪⠜⣼⠿⡼⣿⠐⢂⠒⠒⠒⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⢌⣣⣷⢻⡶⣥⣣⣜⣼⣣⡷⣌⡱⣊⠴⣉⠦⣱⠃⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⠀⠀⠀⠀⠀⠀⡟⠻⣽⣎⡳⣞⠱⣊⣿⡟⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣉⢷⡹⣇⠿⣎⣿⣹⡏⣷⢹⡹⢿⣶⢇⣿⡶⡶⢶⣀⣀⣀⣀⣱⣀⢀⡶⣀⡀⠀⠁⠸⣆⠀⠀⠀⠀⠀⢸⢱⡈⡹⣁⠏⡸⢸⣿⣁⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢵⣫⢟⣾⠼⠗⠻⠭⢷⣟⣳⣎⣿⣳⠟⠁⢠⣟⡟⢫⢛⡙⡏⠿⣷⢦⣀⠁⠀⠀⠈⢆⠀⠀⠀⠀⠈⡦⢱⠱⡌⢎⡱⢹⡾⡏⠸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠈⡏⠀⠀⠀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⢈⠇⡎⡴⣉⠞⣌⠛⣿⣳⢶⣤⣄⣀⢣⠀⠀⠀⠀⢳⢡⠓⣜⢢⡙⣜⠇⣇⢀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠙⣄⠀⠰⢈⡟⠈⠁⠒⠒⠒⠦⠤⠤⣽⡞⣯⠼⣴⡱⣌⡲⣌⢣⣇⣟⣤⣉⣛⣾⢻⠀⠀⠀⠀⠀⢣⡋⡔⢣⠜⣸⣀⡿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⠀⠀⠀⢸⡙⢯⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢼⣛⡶⣝⢧⡟⣾⣹⢯⣟⡶⣫⢗⡞⣯⢻⣆⠈⢂⠈⡄⣿⢞⡯⣷⠃⠀⡇⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢠⡿⡘⢆⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠚⠓⠛⠿⠋⠉⠛⢿⣾⢷⣯⢞⣟⣿⣴⣳⣏⣾⠵⠋⠀⠀⣿⣿⡟⣗⡖⣖⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠉⠉⠛⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⢶⠦⣤⣤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠈⢙⠓⠒⠶⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣀⠀⠀⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⣀⠀⠀⣶⣤⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⣼⢿⣷⣸⣿⣟⣿⣆⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠻⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⣀⠀⢰⡟⠛⢿⣿⣿⡿⠟⢻⣼⡏⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⣯⠀⢸⣷⡞⠋⠉⠀⠀⠀⠀⣿⣷⠀⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⣿⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣿⣧⠶⠒⠛⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⠀⠀⠀⠀⢹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⢞⣩⡶⠂⡀⠀⠀⠀⠀⢀⡇⠀⡟⠀⠀⠀⠀⠀⠀⢠⡾⣿⠋⣀⣤⣴⠾⣿⣧⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡟⣱⣾⠿⠁⣴⣇⠀⠀⠀⠀⢸⡇⢸⣧⡶⠞⠻⠆⠀⠀⠀⠸⠃⠈⣿⣿⣿⣧⣘⣿⣆⠀⠀⠀⠀⠀⠀⠀⢸⡜⡇⠀⠀⠀⠀⠀⠈⠙⢦⣄⣀⠀⢀⣀⣤⠾⢛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣟⣼⣿⡟⠀⣼⣿⢻⡀⠀⢰⡀⢸⡇⣼⣇⣤⣤⣤⣆⡀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⢸⣿⡄⠀⠀⠀⠀⠀⠀⠘⡇⢷⢠⠀⠀⠀⠀⠀⠀⠀⢀⣉⣙⣋⣩⣤⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢻⣿⣿⠀⢰⣿⠻⣧⣧⠀⢸⣇⢸⣷⡏⢿⡟⢿⣿⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢀⡀⠀⠀⠀⡄⠀⡇⠰⠀⡆⠀⠀⣦⠀⠰⣦⡈⠻⢻⣿⣟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⢾⣿⣿⠀⣼⣿⠀⣿⣿⣆⠸⣿⣼⡿⠀⠈⢷⠘⠛⠉⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢸⡇⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⣿⡄⠀⣯⠻⣆⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣯⣿⠀⣿⡿⠀⢹⣞⢿⣆⢻⡽⡇⠀⠀⠸⣇⠀⠀⠀⣏⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣼⣿⠀⠀⢰⣿⡀⡇⠀⠀⠀⡇⢠⡿⡇⠀⣿⣶⠾⠶⣦⣭⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣠⣷⡿⣆⢿⡇⠀⠀⢻⡄⠻⣦⢷⡄⠀⠀⡀⢹⡄⠀⠀⠉⠛⠟⠀⢀⣀⣤⣶⠟⠃⠀⢰⣿⠃⣿⠀⠀⣼⢹⣿⡇⠀⠀⢀⡇⣸⠀⡇⠀⣿⡏⢀⣤⡾⠛⠉⠛⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠴⠾⠿⠏⠙⠉⠀⠹⣾⣇⠀⠀⠀⠻⣆⠈⠻⢿⣄⠀⣿⣆⡻⣆⠀⠀⠰⠶⢿⡭⠵⣞⡁⠀⠀⢀⡿⣱⣿⡿⠀⣸⡇⠈⣿⠁⠀⠀⣼⢷⡏⢠⡇⢼⡟⣣⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣷⣄⠀⠀⠀⠀⠀⠀⠙⢿⡀⠀⠀⠀⠙⢷⡄⠀⠉⠀⡿⣿⣧⢹⣷⣄⠀⠀⠀⠐⠛⠋⠀⠀⠀⠟⣴⡿⣿⠃⣴⠏⣇⠐⠛⠀⠀⢠⡟⠘⠀⠸⠃⣼⣵⡟⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢻⣗⣀⠀⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⢻⡄⠀⢠⡇⠿⢹⣼⡀⠙⠳⣦⣀⠀⠀⠀⠀⠀⣀⡾⠋⣸⣏⣾⡃⠀⢻⡀⠀⠀⢀⣄⠀⠀⢰⡇⢠⣿⡿⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢀⣾⠇⠀⣾⡏⣿⣤⠀⠀⣙⠻⢦⣤⣤⠾⠋⠀⣴⢿⡋⠉⠀⠀⠸⡇⠀⠀⢸⣿⠀⠀⣸⡇⣾⢻⡇⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⢻⣿⣾⠟⢷⡀⣿⣆⢶⡀⠀⠀⣷⢦⣄⡈⢿⣤⣀⠀⠀⣿⠀⠀⣾⣿⠀⢠⣿⣻⣿⢸⡇⠀⠀⠀⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡟⠁⣠⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠈⠿⠃⠀⠀⢸⢸⣿⣻⣶⣶⢿⣼⡿⣾⣧⡀⠀⢸⡎⣿⡿⣷⠟⠙⢷⣄⢸⡇⢠⣿⣿⢀⣾⢻⣿⠃⣶⣿⡀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠲⠶⣶⡶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣻⣶⠶⠲⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⣤⠿⣠⣾⣿⡇⠀⢠⡄⠀⠀⠀⢸⡟⢦⣀⠀⠀⣿⠀⠀⣿⢸⣿⣿⣿⣿⣄⠻⣧⠙⣿⣧⢸⣷⣇⢿⡗⣿⡷⠀⠀⠙⣿⣇⣼⣿⣯⣾⠟⡾⠃⠀⣿⡘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠈⠛⠶⣤⣀⠀⠀⠀⠀ ⠀⠻⠶⠟⠛⣿⡇⠀⣼⡇⠀⠀⠀⢸⣷⣤⣽⣦⠀⣿⡇⢠⡿⣿⡟⣬⣽⡿⠛⠀⠈⠀⠀⠹⣾⡏⢛⡿⠁⠘⣿⡄⠀⢠⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢹⣷⠹⣷⡀⠀⠘⠛⠛⣒⣶⢦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⣤⣄⡀⠀⣰⠟⠁⠀⠀⠀⢀⣠⡶⠀⠀⠀⠀⠙⠳⣄⠀⠀ ⠀⠀⠀⠀⢰⡿⠃⢀⣴⣿⡆⠀⠀⢸⣧⣴⣶⣿⣧⡿⣿⣸⣇⣿⠁⠀⠀⠀⠀⠀⣀⣀⣤⠴⠿⡷⢿⣅⠀⠀⣮⣻⣶⣄⣿⠟⢻⣿⡇⠀⠀⠀⠀⠀⠀⢻⣆⣉⣻⣦⣀⣀⣼⠋⠙⣧⠀⠈⠉⢛⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠿⠦⣤⣄⣠⡴⠿⠷⠚⠛⠃⠀⠀⠀⠀⠈⠳⣄ ⠀⠀⠀⠀⣾⣠⣴⣿⣿⣿⡟⠀⣦⢸⣿⣻⣿⣿⣟⡇⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠉⣁⣀⣀⣀⣷⠀⠙⢧⣴⢾⣿⣿⠟⠁⠀⠀⣿⣿⣄⣤⣶⣢⣤⣤⣼⣿⠁⠠⣭⣉⣹⠃⠀⣰⢸⣆⣠⣴⠿⠋⠀⠉⠙⠳⢶⣤⣀⠀⠀⠀⢀⡿⢀⣠⡴⠞⠋⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠛⠛⠋⠉⠉⢹⣿⢀⣏⢸⣧⠉⠙⠋⠉⠁⠛⢻⠀⠀⠀⠀⠀⠀⠀⢀⣬⡉⠉⠁⠀⣿⠀⠀⢠⣿⣧⣈⠻⢿⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⠟⠁⠙⢷⣄⠨⢷⣿⢠⣤⣯⡴⠛⠉⢹⣧⣀⡀⠀⠀⠀⠈⢷⣍⣛⣷⣦⡾⠟⠋⠁⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⣿⣿⣿⣇⠀⢠⡄⠀⠀⠘⢧⣴⡿⠀⠀⢀⣴⢟⣽⣿⠏⠙⣻⡇⠀⠀⣸⣧⠈⢿⣿⣦⡘⣿⣿⣿⣿⠿⠛⠁⣼⡏⠀⠀⠀⠀⠙⢷⣾⡇⢀⣾⣯⣀⣴⢟⡋⠁⢹⣇⣠⣤⡶⠾⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢸ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣿⠿⠏⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⡑⠆⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⣀⣀⣀⣙⣿⣿⣿⣷⣦⣄⠀⠈⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣧⠐⠀⢻⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⢾⠃⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢹⣾⣷⢈⣩⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠠⠄⣉⠉⠛⣛⣿⣿⣿⣿⣿⣿⣿⣦⣜⣿⣿⣦⠰⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣄⡈⠻⣿⣿⣇⠀⠀⢿⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⢻⢤⠀⠀⢹⣷⡡⠃⠀⠀⠀⠀⠀⠀⣀⣀⣶⣿⣿⣿⡿⠿⠛⠃⠄⠀⠀⠀⠀⠀⠀⢀⣸⣿⠀⠀⣀⢀⣤⡿⠟⠉⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣷⡈⠀⠀⠀⠀⠀⠀⠀⠀⠠⢬⠿⠻⢷⣾⣿⣿⣆⠣⠘⣿⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣤⠀⣤⠀⢻⣿⡙⢀⡀⠀⠀⠀⣜⠿⠉⠩⠿⢿⣿⣧⢩⢀⡀⠀⠀⠀⠀⠀⠀⠀⢈⢹⣿⣄⣧⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣷⡇⡐⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠙⢛⣿⣶⣤⣹⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣦⣄⣬⣻⣿⣿⣱⣤⣄⢀⠟⣆⡀⢀⣃⣸⣿⣿⣿⣿⢆⡀⢠⣅⠀⠀⠀⢠⣄⣼⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⢿⣿⣿⣿⣿⣦⣤⠀⣂⢀⣀⣀⠀⠈⣠⣴⣶⣶⠀⢘⣻⡇⢹⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⣾⣿⣁⣰⣾⣿⣿⣿⣿⣷⣿⣷⣀⢫⣿⣿⣶⡾⠟⠉⣿⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡏⣿⠙⠿⣿⣿⣿⣿⣤⣤⣤⣴⣿⣿⣿⣿⣿⣧⣬⣿⢇⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣿⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣾⠁⣿⠀⠀⠘⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣿⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⡏⠀⠀⣠⡾⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣠⡿⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⢠⡿⠀⠀⠀⣾⠀⢀⣼⠋⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠙⢷⣄⡀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠉⠁⠀⠀⣼⠃⣴⠟⠁⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠶⠚⠳⢾⣿⣦⡀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⢀⣼⣯⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠈⢿⡿⣦⡀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⡿⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⣯⣤⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡌⠻⣆⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠋⠁⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠙⣦⣠⣴⠾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠘⣧⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣧⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠟⠛⠛⠛⠛⠷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⣤⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠿⠙⠙⠛⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠉⠙⠛⠻⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀⠀⠀⠀⠈⠉⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⢰⣿⣿⣦⢠⣿⣯⡿⢷⣆⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⣾⣭⣿⣿⣿⣿⢿⣷⣿⣿⣇⢹⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⣼⠃⣿⣿⢠⡿⢷⣄⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠘⠋⣾⣿⢫⣿⠁⣰⡟⠘⣧⠀⠙⠁⠀⠀⠀⠾⠃⠛⠀⢀⠛⠀⣼⣷⣿⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⢀⣿⠀⡏⢻⣼⡇⠈⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠏⢠⣿⣃⣾⣏⠀⠀⣿⡄⠀⠀⠀⠀⣤⠀⠀⠀⢠⣿⠀⢰⣿⣿⡏⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⣾⣿⠀⠀⣾⡿⢻⣦⡀⠀⠈⠙⠻⣶⣄⣀⠀⣀⣴⡾⠋⠁⢀⣿⡿⠛⠛⠋⠀⠀⢸⣇⠀⠀⠀⢀⣿⡇⠀⠀⢸⣿⠀⣾⡏⣿⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⠃⠀⠀⣿⣷⣘⣿⣿⣆⠀⢸⣧⡀⢉⠛⠛⠋⠉⣠⣄⠀⠉⠉⢿⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⡇⠀⠀⣾⣿⣰⡿⠁⣿⠀⠀⠀⠀⠹⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠃⠀⠀⡀⢹⡏⣿⣿⠁⠹⣧⡀⣿⣧⠸⣷⠀⠀⠀⠸⣿⢻⣶⣤⡈⠻⣷⣦⣄⠀⠀⢹⡇⠀⠀⣾⣿⡇⠀⣰⣿⣿⣿⡇⠀⣿⡆⠀⠀⠀⠀⠀⠉⠛⠷⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⡿⠁⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠀⠈⠿⠟⠀⠀⠀⠀⣷⠸⣿⢟⣿⣶⣶⡿⣷⣽⡟⣷⣿⣧⠀⠀⠀⣿⡈⣿⣿⢿⣿⠟⠉⠻⣷⣄⠘⣧⠀⢸⣿⣿⡇⢠⣿⢿⣿⣿⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠲⢶⣶⡒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣛⣷⡶⠟⠓⠶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⡟⢀⣴⣿⣿⡆⠀⠀⣠⡀⠀⠀⠀⠀⢸⣿⢷⣄⠀⠀⠀⠰⣶⠀⠀⢠⣿⠀⣿⣾⣿⣿⣿⡇⠹⢿⣇⠘⣿⣿⣇⢸⣷⣼⡇⣼⣿⢾⣿⡷⠀⠀⠈⠻⣷⣿⢀⣾⣿⣿⣳⣿⠟⣷⡿⠁⠀⢿⡇⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠛⠉⠀⠀⠀⠀⠈⠙⢻⣦⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⢸⣏⣀⣿⣿⣿⣿⡇⠀⢀⣿⡇⠀⠀⠀⠀⢸⣿⡀⠙⢷⣄⠀⢰⣿⡆⠀⣾⣿⣆⣿⡟⠻⣿⣿⣿⡖⠈⠛⠂⠈⠙⢿⣬⣿⠿⣿⣽⡏⠈⢿⣷⠀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⠏⠀⠉⠁⠀⠀⢸⣿⡈⣿⣦⠀⠀⠀⠰⣶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⢶⣤⣀⣀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠉⠻⢷⣤⡀⠀⠀⠀ ⠀⠀⠉⠉⠁⠀⢹⣿⡇⠀⠘⢻⣇⠀⠀⠀⠀⢸⣿⠛⠛⠻⣿⣦⢈⣿⣷⠀⣿⠙⣿⡇⠛⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⢿⣿⠀⣰⡟⠀⠀⠀⠻⣷⣄⠀⠸⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⣿⣷⠘⣻⣷⣄⠀⠀⠀⠀⣠⣼⢿⣟⠛⠛⠶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⣦⣄⣀⣾⠃⠀⠀⠀⠀⠀⣀⣴⣾⣛⣀⣀⡀⠀⠀⠀⠀⠈⠻⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⣿⠿⠀⢀⣴⣿⣿⡇⠀⠀⠀⢸⣿⣶⣿⣿⣿⣿⣾⡟⣿⣶⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⡶⠞⠻⣿⠟⢻⣦⡀⠀⠘⢷⣿⣿⣷⣤⣾⡿⠋⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣤⣬⣿⣶⣄⣀⣰⡟⠁⠀⢻⡆⠀⠀⠀⠈⣩⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠛⠳⢶⣶⣤⣤⣾⠟⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦ ⠀⠀⠀⠀⠀⣴⡏⣠⣴⣿⣿⣿⢿⡿⠀⢸⡄⢸⣿⡟⢿⣿⣿⡿⢹⡇⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⣀⣀⣸⡇⠀⠙⢿⣄⣾⣿⣿⣿⡿⠟⠋⠀⠀⠈⢿⣿⣧⢀⣀⣴⣾⣀⣤⣤⣤⣿⣟⠁⠀⣤⡍⣉⣹⡟⠀⠀⢠⡎⣿⣀⣀⣤⣾⠿⠋⠀⠈⠉⠛⠿⢶⣦⣄⡀⠀⠀⠀⠀⠀⣼⡏⠀⣀⣤⡶⠿⠛⠛⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⡿⠟⠛⠛⠛⢸⣿⠀⢸⡇⢸⣿⠙⠛⠿⠿⠛⠛⠁⣿⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠛⠛⠋⠉⢹⡇⠀⠀⠀⢹⣿⣌⠙⠻⣿⣶⣤⣀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢿⣦⡀⠈⡻⣯⣿⡇⠀⢀⣿⢃⣽⡿⠛⠻⣿⡀⠀⠀⠀⠀⠀⠀⠘⢻⣯⡛⢿⣶⣤⣄⣠⣿⡶⠟⠛⠁⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢀⣾⣷⣼⣿⣷⡀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢀⣠⡄⠀⠀⠀⠀⣠⣾⢿⣷⣤⣤⣤⣄⣼⠃⠀⠀⢠⣿⡋⠻⣷⣦⣀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣿⡿⠁⠀⠀⠀⠙⢿⣦⡀⣼⣿⠁⠉⣿⡿⠟⠁⢀⣠⣴⡿⠿⢿⣷⠀⠀⠀⠀⣀⣀⣭⣿⣶⠾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢼⣿⣿⡿⣿⣿⣅⠀⠰⠿⠀⠀⠀⠀⠙⠿⢿⣿⠁⠀⠀⣠⣾⢟⣵⣿⣿⡿⠀⠀⢸⡿⠀⠀⠀⣠⣿⣷⡀⠘⠿⣿⣷⣦⣿⣿⣿⣿⡿⠟⠋⠁⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠙⠿⢿⣿⣀⣼⡿⠷⠤⣴⣿⠫⣤⠀⠀⣸⣿⣴⡶⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠟⠻⣷⡾⠿⢿⣿⡀⠀⣠⡿⠀⠀⠀⠀⠀⣀⣤⣴⢟⣫⣶⣿⣿⣿⡿⠁⠀⢠⣿⠁⠀⠀⢸⣿⠟⠛⢿⣿⣀⠀⠙⢿⣿⡟⠋⠁⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣿⣿⡇⠀⢰⣿⡏⠀⠀⣠⣾⣿⠋⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣾⣿⠀⠀⣦⠿⢿⣿⣯⣵⣿⣿⣿⣟⣯⡾⠟⠀⠀⢀⣾⠃⠀⢀⣴⣿⣿⣶⣄⠀⠙⠻⣷⣤⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⢠⣿⣿⠃⢀⣾⣿⡿⠇⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡴⠶⠾⢿⣿⠛⠃⢀⣀⢀⣴⣶⡾⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣟⢀⡀⠉⠛⠿⠷⠛⢛⣋⣥⡶⠀⠀⢠⡾⠃⠀⠀⢸⣿⡍⠀⠙⠿⣿⣦⣀⢉⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠿⣶⡿⣿⡃⣠⣾⣿⠟⣣⣴⣿⣿⣄⠀⠀⠀⠀⢀⣀⣠⣤⣤⡤⠶⠶⠞⠛⠛⣛⣩⣭⣭⣤⣶⣶⣾⣿⣿⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⡷⣦⣀⠀⠀⠉⠉⠁⠀⢀⣼⠟⠁⣀⣤⣤⣼⣿⣷⣄⡀⠀⠻⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠻⣿⣦⡈⠻⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣦⣄⣛⣋⣉⣭⣤⣤⣶⡶⠾⠿⠿⣿⣏⠉⠉⠉⠀⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⣾⣧⡈⠉⠻⣷⣦⣤⣤⣴⣿⣭⣤⣴⣿⣿⣿⣯⡉⠻⣿⣿⣦⣄⢰⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠻⣿⣦⡈⣿⣿⣿⣿⣿⠇⢹⣿⡏⢻⣿⡏⠛⠛⢿⣿⣍⠉⠉⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣇⠀⢻⣿⣷⡀⠀⢻⣿⣿⣿⡿⢻⣿⣯⣿⣿⣿⣿⣿⣷⡀⠘⢿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣌⠙⢿⣶⣶⣿⣿⠃⣸⣿⠁⠀⠀⣀⣽⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡀⠙⣿⡀⠀⢿⣿⣷⡄⠈⣿⣿⣿⣿⡘⢿⣿⣿⢻⣿⣿⡜⣿⣿⣆⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⣙⣿⣯⣴⣾⡿⠋⠀⢠⣾⣿⠿⣿⣿⣶⣄⣀⣀⡀⠀⠀⠀⠀⣽⣿⣆⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣸⡇⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⢠⣿⠁⠀⠀⣠⣿⠋⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠆⠀⠀⠀⣰⡿⠁⠀⠀⠀⣼⡏⠀⣠⣾⠟⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠉⠁⠀⠀⠀⣼⡟⢀⣴⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣤⣤⣤⣬⣝⣷⣤⡀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠉⠀⠀⠈⠙⠻⣯⣿⣦⡀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⢿⣦⡀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⠶⠶⠶⠶⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠙⣷⡄⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠈⢻⣆⠀⢀⣴⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⢻⣿⠛⠋⠁⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢻⣧⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⢻⣧⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡽⠙⠉⠚⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣣⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⢏⠛⠚⠂⠾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠬⠂⠀⠛⡋⠒⠴⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⢲⣟⣛⠀⠀⠈⠢⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢀⡴⣼⠷⠀⠀⠀⠀⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢃⠀⠀⠀⠀⠀⠠⡧⣬⠇⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠏⠁⠀⠀⠀⠀⠀⢸⣟⣻⠀⠀⠀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⠴⠀⠀⠀⠀⠀⠀⢡⠀ ⠀⠀⠀⠀⠀⠀⠀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⡻⠗⠀⠀⠀⠀⠀⠀⠀⡀ ⡀⠀⠀⠀⢀⣴⡧⣤⣤⡄⣤⢠⡴⠀⠀⠀⠀⠀⢀⢴⣿⢗⣿⠀⠀⠀⠀⠀⠀⠀⠇ ⣿⣆⠀⣰⣿⣿⣿⣿⣯⣿⣛⣴⠀⣀⠀⠀⠀⠠⠃⢘⠟⠒⠋⠀⠀⠀⠀⠀⠀⡀⢸ ⣿⠏⠰⠀⠀⠉⠻⢿⣿⣿⣿⣿⣼⡷⠀⣠⢠⠃⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⢸ ⠁⠀⠀⡇⣀⠴⠊⠁⠈⠙⢿⣿⣿⣿⣽⣏⣬⣶⡎⠀⢀⠀⣰⠀⠀⠀⠀⢠⢱⠀⢸
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